Problem 4: Differential Analysis Water flows in a thin layer between a wall and a vertical plate separated by a distance h = 1 mm. The wall is stationary while the plate moves upwards with a velocity Vplate = 1 m/s. Assume p=1000 kg/m³, v = 10-6 m²/s. 1. Assuming that the flow is laminar, steady, and fully developed, use differential analysis (Navier-Stokes) to calculate the velocity profile. 2. Calculate the flow rate per unit width. 3. Compute the Reynolds number in the water and air flow and determine if the conditions are laminar or turbulent. b-1 mm g-10 Pam Zoomed-in fully-developed region V-1 m/s Figure 4: Flow between stationary wall and moving plate.

6) Air flow though the device shown in figure. Select which set of the following conditions is TRUE assuming incompressible non-viscous steady flow (a) p4 v3 (c) p2>p3; v2 > v3 (e) p4> pl; v4 pl; v1 > v3 (d) p4 vl "OUT

An incompressible viscous flow is contained between two parallel plates separated from each other by distance b. as shown in Figure 1. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U =7 m/s and b= 1 cm, and there is no pressure gradient in the flow direction. A.) Start with Navier-Stokes equations and determine the velocity at the point x = 3 cm and y= 0.41 cm. The value of the velocity is.B.) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity. C.) Calculate the rate of angular deformation at the same point. The angular deformation value

Oil Coating: A long, continuous belt is pulled upwards through a chemical oil bath at velocity V0. The belt has rectangular cross-section and has length (L), width into the paper (W). The belt picks up a film of oil of thickness h, density ρ, and dynamic viscosity μ. Gravity g tends to make the oil drain down, but the movement of the belt keeps the fluid from running off completely. Assume fully developed, steady, laminar, incompressible and two-dimensional flow of oil to answer the following questions. Assume that no pressure gradient is needed in the vertical direction to drive the film flow. Also assume that the shear stress at the air-oil interface is zero (free shear condition). Assume no-slip condition for the fluid in contact with the moving belt. Justify any other assumptions you may make. Show all steps. (a) Derive an expression for the two-dimensional velocity field inside the oil film in terms of the known parameters. Clearly indicate your co-ordinates and origin. You must…